I need help for the study of this function, please

[Lady_Athena.]

The function is xe^(1/x + x)
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[/FONT]The domain is R\{0}

The sign y>0 so x>0 (before 0 is negative and after is positive)

The derivative and its sign was quite easy.

But I'm having problems evaluating the limits of this function (in order to find asymptotes).
Could you please show me how to do the limits step by step? I have already a general idea of it, but I'm afraid of skipping some important steps.

And one last thing.. I would like to know if this function is invertible... (I can not really understand how to invert a function.. so if you could explain it to me I will really appreciate it)

Thank you for your help!

 

[stapel]

The function is xe^(1/x + x)

This is not a "function", as there is no "equals" nor any functional name.
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The domain is R\{0}

Yes. Were you asked to find the domain, or were you given that this is the domain, or are you for some reason just stating the domain?

The sign y>0 so x>0 (before 0 is negative and after is positive)

You have no "y" in your original expression. Did you mean the following?

. . . . .\(\displaystyle y\, =\, x\, e^{\left(\frac{1}{x}\, +\, x\right)}\)

Also, what do you mean by "so x>0"? The input variable can most definitely be negative!

The derivative and its sign was quite easy.

Since this "was quite easy", obviously you're in calculus, having completed algebra, trig, and/or pre-calc. Were you asked (by some unstated instructions) to find the derivative?

But I'm having problems evaluating the limits of this function (in order to find asymptotes).

Which limits? Which asymptotes?

Could you please show me how to do the limits step by step?

Didn't your book have an entire chapter on limits, before your class got to derivatives?

I have already a general idea of it, but I'm afraid of skipping some important steps.

Then please reply showing your work, and we'll be glad to help you fill in the gaps, if any.

I would like to know if this function is invertible... (I can not really understand how to invert a function.. so if you could explain it to me I will really appreciate it)

Working with functions, including composing and inverting them, was supposed to have been covered back in algebra and pre-calc (such as inverse-trig functions)...? :shock: